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Adapting stopping patterns to improve robustness from the users’ perspective
Jens Parbo
PhD student
Technical University of Denmark
2 DTU Transport, Danmarks Tekniske Universitet
Outline
• Introduction & motivation
• Skip-stop optimisation
• Results
• Summary
3 DTU Transport, Danmarks Tekniske Universitet
Outline
• Introduction & motivation
• Skip-stop optimisation
• Results
• Summary
4 DTU Transport, Danmarks Tekniske Universitet
Introduction & Motivation
• Stopping patterns of railway lines have a large impact on travel time, but also on system-wide delays
• Applying skip-stop optimisation intelligently enables:
– The benefits of skip-stop services (reduced travel time)
– Reduced heterogeneity (i.e. operation less vulnerable to delays)
• Homogeneous (solid lines) vs. heterogeneous (dashed lines) operation
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Tim
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Stop
5 DTU Transport, Danmarks Tekniske Universitet
Outline
• Introduction & Motivation
• Skip-stop Optimisation
• Results
• Summary
6 DTU Transport, Danmarks Tekniske Universitet
Skip-stop Optimisation
• Bi-level optimisation
Passengers’ travel behaviour
Railway lines’ stopping patterns
7 DTU Transport, Danmarks Tekniske Universitet
Mathematical Model (Upper level)
• Finding optimal stopping patterns.
8 DTU Transport, Danmarks Tekniske Universitet
Public assignment model (Lower level)
• Deriving passengers’ travel behaviour.
• Utility-based approach.
9 DTU Transport, Danmarks Tekniske Universitet
Heuristic solution algorithm - Framework
1. Run public assignment.
2. Calculate optimisation potential for each skip-stop.
3. Calculate elaborate optimisation potential for the most promising skip-stops (2)
4. Impose skip-stops.
5. Prohibit skipping stops in the sub network for imposed skip-stops
6. If stopping criterion met, stop.
7. Otherwise, go to (1).
Inner lo
op
10 DTU Transport, Danmarks Tekniske Universitet
• When skipping a stop on a line, trips to/from the considered station within the corridor are separated in 3 types.
• Benefit: reduced in-vehicle time (2 min.)
• Trip 1 costs (Waiting time)
• Trip 2 costs (Waiting time + Transfer time)
• Type 3 trips are PROHIBITED!
• Trips from outside the corridor (Waiting time)
Heuristic solution algorithm – Elaborate optimisation potential
11 DTU Transport, Danmarks Tekniske Universitet
Heuristic solution algorithm - Tackling overtaking and heterogeneity
• Limitation on the number of skipped stops between parallel lines when considering the stops sequentially.
• Conflicts between railway lines from different corridors can be handled by adapting depature times or adding buffer time.
• Reduced capacity utilisation as a result of more homogeneous operations.
Line A
Line A
Line B
Line B
12 DTU Transport, Danmarks Tekniske Universitet
Outline
• Introduction & Motivation
• Skip-stop Optimisation
• Results
• Summary
13 DTU Transport, Danmarks Tekniske Universitet
• Passengers are marginally better of compaired to the existing situation.
• The small reduction in Generalised travel cost is misleading
Results - Passengers’ travel cost
Percentage change (Final solution)
Changes In-Vehicle Time Generalised Cost Waiting Time
Relative to existing stoppping pattern -0,18 1,01 0,09 1,66
Relative To All-stop Base -1,51 5,46 1,76 -1,67
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Iteration #
Transfers
In-Vehicle Time
Generalised Cost
Waiting Time
14 DTU Transport, Danmarks Tekniske Universitet
• Existing vs. optimised
– Time-space diagrams
– Line diagrams
• Optimised -> homogeneous
– More buffer time
– Delays are absorbed
Results - Heterogeneity of railway operations
Optimised Existing
Optimised Existing
15 DTU Transport, Danmarks Tekniske Universitet
• Number of skipped stops per line in each corridor.
– Average
– Standard deviation
• SSHR (heterogeneity) values for each corridor.
• All-stop scenario serves as LB on SSHR.
Results - Heterogeneity (Continued)
16 DTU Transport, Danmarks Tekniske Universitet
Outline
• Introduction & Motivation
• Skip-stop Optimisation
• Results
• Summary
17 DTU Transport, Danmarks Tekniske Universitet
Summary
• Skip-stop optimisation solved as a bi-level optimisation problem taking passengers’ travel behaviour explicitly into account.
• Reduction equal to 1.01 % in in-vehicle time and 1.66 % in waiting time was obtained compared to existing network.
• Heterogeneity significantly improved in all corridors (5-55 %).
• Consequently, passengers get faster and more reliable from A to B.